In mammals, place cells and grid cells in the hippocampal formation seem to code for the location of animals in space (Hartley et al. 2013). They do so by becoming active in certain, roughly circular, regions of the environment known as the cell’s ‘place fields’. Interestingly, when an animal is entering a cell’s place field, the cell will fire at the late phases of an ongoing oscillation that can be measured in the local field potential. As the animal then progresses through the field, firing will occur at earlier and earlier phases, a phenomenon known as phase precession. If we now look at a population of such uniformly precessing cells with place fields scattered through the environment we will see cells firing sequentially within each cycle of the oscillation: cells with place fields centered behind the current position of the animal will fire first, followed by cells with place fields centered progressively more ahead. This way, within each cycle, the population represents in a compressed manner a piece of the trajectory of the animal centered around its current position.
In the past decades, a relatively large number of experimental findings have been reported regarding these phenomena, but a quantitative model integrating the results and clarifying the relationships between different relevant variables is still lacking. For instance, what is the relationship between running velocity, the extent of the trajectory represented within each cycle, and the place field size? Or, what is the relationship between phase precession in single cells and the sequentially organized activity at the population level? In this project we will look at these issues through a combination of mathematical analysis and simulations. Some programming experience is required.
Hartley, T., C. Lever, N. Burgess, and J. O’Keefe. 2013. “Space in the Brain: How the Hippocampal Formation Supports Spatial Cognition.” Philosophical Transactions of the Royal Society B: Biological Sciences 369 (1635): 20120510–20120510. https://doi.org/10.1098/rstb.2012.0510